20.4.25 problem Problem 41

Internal problem ID [3660]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 41
Date solved : Monday, January 27, 2025 at 07:52:41 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+\frac {2 y}{x}&=6 \sqrt {x^{2}+1}\, \sqrt {y} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 38

dsolve(diff(y(x),x)+2/x*y(x)=6*sqrt(1+x^2)*sqrt(y(x)),y(x), singsol=all)
 

\[ \frac {-x^{2} \sqrt {x^{2}+1}+x \sqrt {y \left (x \right )}-c_{1} -\sqrt {x^{2}+1}}{x} = 0 \]

✓ Solution by Mathematica

Time used: 0.240 (sec). Leaf size: 55

DSolve[D[y[x],x]+2/x*y[x]==6*Sqrt[1+x^2]*Sqrt[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^6+3 x^4+x^2 \left (3+2 c_1 \sqrt {x^2+1}\right )+2 c_1 \sqrt {x^2+1}+1+c_1{}^2}{x^2} \]